Vibrating element sensors may be used to measure pressure, density, force, viscosity and temperature. An example of such a sensor is described in GB 2,413,386. Examples are also the Weston 7881 pressure sensor and Weston 7825 fuel densitometer both manufactured by Weston Aerospace limited. Embodiments of the invention could also be used with Doppler radar where the frequency is proportional to the velocity of an object.
Vibrating element sensors, which include vibrating cylinder pressure and/or density sensors, provide an output frequency that is dependent on the measured parameter (e.g. pressure in a pressure sensor). The remainder of this application will refer to the measurement of pressure; however the same techniques would apply equally to the measurement of any other parameter using a vibrating element sensor, or any other sensor having an output signal with a frequency dependent on an input or measured parameter (for example, Doppler radar).
The sensor's output frequency must be determined or measured accurately, with low noise and sufficient resolution to meet the sensor's performance requirements
The frequency, or period, of the sensor's output signal is measured against an accurate high frequency reference clock. In the example shown in FIG. 1 the reference clock, with frequency Fr, is counted between two falling edges 1 of the sensor's output signal 2.
The period T of the sensor signal in seconds is then given by:
                                          T            =                          Nc                              Fr                ·                Ns                                              ,                ⁢                                                      (        1        )            where Fr is the reference clock frequency in Hz, Nc is the number of clock cycles and Ns is the number of sensor signal pulse cycles.
The resolution of the measured period is determined by the number of reference clock cycles in the measurement period. The resolution can be improved by increasing the frequency of the reference clock Fr, counting over a greater number of sensor cycles Nc (hence increasing the length of the measurement period), or a combination of both.
It is important to differentiate between genuine pressure variations and unwanted noise which does not relate to pressure changes. It is desirable to be able to measure the former but the latter should be minimised. For ease of understanding, the following discussion and explanation assumes the sensor input pressure is constant so that any noise referred to is unwanted and emanates either from within the sensor itself or as a result of external interference.
Noise on the sensor's output manifests itself as jitter on the edges of the measured signal pulses. The signal pulse edges 1 are shifted from their nominal ‘true’ position 3 by a randomly varying time. FIG. 2 shows the effect this has on the period measurement.
The measured time between the start and stop sensor edges 1 is in error by Δt1+Δt2.
Assuming that this jitter error on each edge (Δtn) has a normal (Gaussian) distribution, it can be expressed as an error with standard deviation e. As this appears on both the start and stop edges the error in the measured time is given by:E=√{square root over (e2+e2)}  (2)where E is the standard deviation of the error in the measured time between the start and stop edges.
The ‘root sum of squares’ assumption of equation (2) only holds true if the errors in the start and stop edges are truly independent and there is no correlation between them. As explained later, this hypothesis can be tested by making real measurements.
If the pressure is constant and the noise on each of the edges is independent, then the jitter time on the measurement between any two edges is given by E. If the time measurement is made over Ns sensor cycles, the time error Ep in the measurement of a single sensor cycle period (i.e. the period between consecutive signal pulses) is given by:
                    Ep        =                  E          Ns                                    (        3        )            
The total measurement time t between the start and stop edges of a sampling period is given by:t=Ns.P  (4)
where P is the period of a single sensor cycle.
Rearranging for Ns and substituting in the previous equation gives:
                    Ep        =                              E            ·            P                    t                                    (        5        )            
If the sensor is making repeated measurements that are t seconds apart then the sampling update frequency F is given by 1/t. So the above equation for the time error Ep can by written as:Ep=E.P.F  (6)
So if the noise on an edge is truly independent of the noise on other edges, it should be found that the jitter error, and hence the pressure noise, is proportional to the update rate of the measurement.
FIG. 3 shows an example of noise measurements made on a vibrating cylinder sensor at different update rates whilst measuring a constant pressure.
This shows a strong linear relationship between measurement noise and update rate, validating the hypothesis that the noise on a sensor output edge is independent of the noise on other sensor output edges.
Using the frequency measurement technique described above the known way of reducing the effect of noise has been to increase the sampling or measurement time and hence decrease the update rate. In some cases, where a fast update rate is not required, this is acceptable. However, in other cases, where for example the sensor forms part of a control loop, both a fast update rate and low noise are required.